The described technology is generally directed towards providing a visible waveform representation of an audio signal, by processing the audio signal with a polynomial (e.g., cubic) mapping function. Coefficients of the polynomial mapping function are predetermined based on constraints (e.g., slope information and desired range of the resultant curve), and whether the plotted audio waveform corresponds to sound field quantities or power quantities. Once the visible representation of the reshaped audio waveform is displayed, audio and/or video editing operations can be performed, e.g., by time-aligning other audio or video with the reshaped audio waveform, and/or modifying the reshaped audio waveform to change the underlying audio data.